Temperature-dependent Green Function Research Articles

Permittivity in Molecular Nanofilms

AbstractA microscopic theory of dielectrical properties of thin molecular films, i.e. quasi 2D systems bounded by two surfaces parallel to XY planes was formulated. Harmonic exciton states were calculated using the method of two-time, retarded, temperature dependent Green's functions. It has been shown that two types of excitations can occur: bulk and surface exciton states. Analysis of the optical properties of these crystalline systems for low exciton concentration shows that the permittivity strongly depends on boundary parameters and the thickness of the film. Conditions for the appearance of localized exciton states have been especially analyzed.

Microwave dielectric tangent losses in KDP and DKDP crystals

By adding cubic and quartic phonon anharmonic interactions in the pseudospin lattice coupled mode (PLCM) model for KDP-type crystals and using double-time temperature dependent Green's function method, expressions for soft mode frequency, dielectric constant and dielectric tangent loss are obtained. Using model parameters given by Ganguliet al [9] the dielectric losses are calculated for KDP and DKDP crystals. In the microwave frequency range an increase in frequency (1–35 GHz) is followed by an increase in dielectric tangent loss (1–35) at 98 K and (1–15) × 10−2 at 333 K for KDP and DKDP crystals respectively. The dielectric tangent loss decreases from 0.052 to 0.042 for KDP crystals with increase in temperature from 130 to 170 K and for DKDP crystals it decreases from 0.0166 to 0.0074 with an increase in temperature from 230–343 K in their paraelectric phases at 10 GHz. This shows Curie-Weiss behavior of the dielectric tangent loss

Irreducible Green functions method and many-particle interacting systems on a lattice

The Green-function technique, termed the irreducible Green functions (IGF) method, that is a certain reformulation of the equation-of motion method for double-time temperature dependent Green functions (GFs) is presented. This method was developed to overcome some ambiguities in terminating the hierarchy of the equations of motion of double-time Green functions and to give a workable technique to systematic way of decoupling. The approach provides a practical method for description of the many-body quasi-particle dynamics of correlated systems on a lattice with complex spectra. Moreover, it provides a very compact and self-consistent way of taking into account the damping eects and finite lifetimes of quasi-particles due to inelastic collisions. In addition, it correctly defines the Generalized Mean Fields (GMF), that determine elastic scattering renormalizations and , in general, are not functionals of the mean particle densities only. The purpose of this article is to present the foundations of the IGF method. The technical details and examples are given as well. Although some space is devoted to the formal structure of the method, the emphasis is on its utility. Applications to the lattice fermion models such as Hubbard/Anderson models and to the Heisenberg ferro- and antiferromagnet, which manifest the operational ability of the method are given. It is shown that the IGF method provides a powerful tool for the construction of essentially new dynamical solutions for strongly interacting many-particle systems with complex spectra.

Effect of biquadratic exchange and crystal field anisotropy on the Curie temperature of anisotropic ferromagnet

A spin-1 anisotropic ferromagnet with crystal field anisotropy parameter D and biquadratic exchange interaction parameter α (0⩽ α⩽1) has been investigated using the method of double time temperature dependent Green functions. Mixed Callen and RPA decoupling approximations have been utilized. The variations of Curie temperature T C with α for different values of the exchange anisotropy parameter η (0⩽ η⩽1) at D/ J=1 and for different values of D/ J at η=1 have been studied. Also the value of exchange anisotropy parameter for which dependence of T C on α vanishes has been calculated at finite D. Drawbacks and limitations in the earlier calculations have been pointed out.

Magnon Specific Heat in Quasi-Two-Dimensional Antiferromagnetic Materials: Application to YBa2Cu3O6 and La2CuO4 Oxide Superconductors

The aim of the present paper is to study the magnon specific heat by using the quasi-two-dimensional Heisenberg model and Zubarev's double time temperature dependent Green's function. We used the equation of motion method and the Callen decoupling method to evaluate the double time temperature dependent Green's functions. In antiferromagnetic materials, it is found that there is some axis along which the magnetic moment tends to align with lower energy, due to the presence of anisotropic antiferromagnetic correlation coupling. We study the role of anisotropic antiferromagnetic coupling on the magnon specific heat. Using our theory, we have calculated the contribution of the magnon specific heat in YBa 2 Cu 3 O 6 and La 2 CuO 4 high-temperature superconducting compounds in the antiferromagnetic phase. The role of interlaycr coupling between CuO laycrs has also been studied.

Perturbation expansion for the p-d model around the atomic limit: A study on spin magnetic susceptibility

We propose a nonstandard perturbative solution of the p-d model, based on a generalized cumulant expansion. Using a temperature dependent Green's functions formalism, we investigate the magnetic properties of the model within the second-order perturbation with respect to the hopping term. A qualitative comparison with experiments is discussed.

Cumulant expansion for the p-d model

We propose a nonstandard perturbative solution of the p-d model, based on a generalized cumulant expansion. Using a temperature-dependent Green's function formalism, the effect of the on-site Coulomb repulsion U is taken into account to determine the density of states of correlated electrons, with varying parameters of the Hamiltonian. A qualitative comparison with similar perturbative approaches is discussed.

Calculation of the out-of-plane dynamical correlation for CsNiF3.

The out of plane dynamical correlation function for the one dimensional easy plane antiferromagnet is calculated at low temperatures using a diagramatic expansion for the temperature dependent Green function. The calculation is applied to the compound (CH3)4NM n Cl3 (TMMC).

Cumulant expansion for the p–d model: density of states and hole occupation

We propose a nonstandard perturbative solution of the p - d model, based on a generalized cumulant expansion. Using a temperature dependent Green's functions formalism, the behaviour of the density of states and the hole occupation number is investigated in the charge-transfer and in the Mott-Hubbard regime, to describe realistic systems with CuO2 sheets. A comparison with different analytic and numerical methods is also discussed.

Method of anomalous Green's functions: Antiferromagnetism in the Hubbard model on a triangular lattice

A method is proposed for describing antiferromagnetic and ferromagnetic states on a triangular lattice in the formalism of anomalous temperature-dependent Green's functions, for which equations of Dyson-Gor'kov type are formulated. These equations are solved in the Hartree approximation, and self-consistency equations are obtained for the order parameters. Finally, the connection between the considered theory and experiment is discussed.

Spin-one Heisenberg ferromagnet with three-atom exchange

We study the statistical mechanics of a spin-one ferromagnet with the nearest-neighbour bilinear Heisenberg exchange constant J and the three-atom coupling constant L using the equation-of-motion method for the two-time temperature-dependent Green function. It is seen that, as the three-atom coupling parameter alpha =L/J is increased positively, the Curie temperature TC first increases steeply and then increases very slowly and ultimately approaches the limiting value kBTC/Jz=4/3 as alpha tends to infinity. The situation is much more complicated for negative alpha but, as alpha to infinity , TC approaches the limiting value 4/3. The temperature variation in spontaneous magnetization m and the quadrupolar ordering parameter lambda for various values of alpha are studied. It is seen that there exists a critical value of alpha (which we shall call alpha c) beyond which the phase transition is first order for SC, BCC and FCC lattices. alpha c decreases as the number z of nearest neighbour increases. The discontinuity in m has been found to be extremely sensitive near alpha c. The results are discussed with reference to those obtained by earlier workers.

Theory of the electronic specific heat: Effect of electron-electron interactions

Using a temperature dependent Green's function formalism, we derive an expression for the specific heat of a correlated electron system, and compute the effects of electron-electron interaction on the specific heat. Our results together with other mechanisms, where available, compare well with experimental results in most of the simple metals.

Molecular hydrodynamics of degenerate weakly nonideal bose gas. I. Generalized equations of two-fluid hydrodynamics

A degenerate weakly nonideal Bose gas is investigated at temperatures near zero. Relations connecting the irreducible Green's functions are used to obtain exact expressions for the two-time temperature-dependent Green's functions. In the case of weak nonideality an expression possessing interpolation properties with respect to the frequency and momentum is obtained for the density—density Green's function. At low frequencies, the results of two-fluid hydrodynamics are reproduced. At wavelengths less than the mean free path the energy of the elementary excitations and the damping obtained in the paper agree with the results of perturbation theory with respect to the coupling constant. An expression for the operator of the superfluid velocity is obtained.

Calculation of the out-of-plane dynamical correlation for two-dimensional magnetic systems

The out-of-plane dynamical correlation functionsS zz (q, ω) for two-dimensional easy-plane ferro- and antiferromagnets are calculated using a diagrammatic expansion for the temperature dependent Green function. Vortex-magnon interference effects on the multimagnon and vortex contribution toS zz (q, ω) are also analised, in a classical context, for ferromagnets. Our calculations show that we cannot expect multimagnon processes to contribute to a central peak (ω=0) that has been observed in these systems for temperaturesT>T c , whereT c is the temperature at which a topological phase transition is predicted to occur. However, vortex-magnon interactions considerably reduce the intensity of the vortex induced central peak.

Neutron scattering in impure anharmonic solids

The Debye-Waller factor and the coherent inelastic differential scattering cross section for the one- and two-phonon band modes have been investigated for an anharmonic crystal containing randomly distributed substitutional impurities of low concentration. The method adopted in the evaluation is that of double time temperature dependent Green's functions. The quantities thus evaluated have been separated into diagonal and nondiagonal terms. The diagonal terms are further separated in three contributions, namely the contributions from defects, anharmonicity, and simultaneous involvement of impurity and anharmonicity. A new mode, the “impurity-anharmonicity interference” mode, is the salient featue of the theory, and arises due to the interaction between local and anharmonic fields.

Calculation of the out of plane dynamical correlation for TMMC

The out of plane dynamical correlation function for the one dimensional easy plane antiferromagnet is calculated at low temperatures using a diagramatic expansion for the temperature dependent Green function. The calculation is applied to the compound (CH3)4NM n Cl3 (TMMC).

Neutron star properties and the relativistic nuclear equation of state of many-baryon matter

A relativistic model of baryons interacting via the exchange of σ-, ω-, π- and ρ-mesons (scalar-vector-isovector (SVI) theory) is used to describe the properties of both dense and superdense matter. For the theoretical frame, we used the temperature-dependent Green's function formalism. The equation of state (EOS) is calculated for nuclear as well as neutron matter in the Hartree (H) and Hartree-Fock (HF) approximation. The existence of phase transitions has been investigated. The isotherms of pressure as a function of density show for nuclear matter a critical temperature of about T c HF = 16.6 MeV. (As in the usual scalar-vector (SV) theory, the phase transition is absent for neutron matter. A phase transition of both many-baryon systems in the high-pressure and high-density region, which has been found within the SV many-baryon theory, appears in the SVI theory too. The calculated maximum stable masses of neutron stars depend on (1) the underlying parameter set and/or (2) on the chosen approximation (i.e., H, HF; SV-, SVI theory, respectively). Hartree calculations lead to amass stability limit of M max H ⩽ 2.87 M ⊙ ( M max H ⩽ 2.44 M ⊙ when hyperons are taken into account). For the HF calculations we obtained M max HF ⩽ 3.00 M ⊙ ( M max HF ⩽2.85 M ⊙). The corresponding maximum radii are (same notation as above) R H ⩽ 13.2 km ( R H ⩽ 11.8 km), R HF ⩽ 14.0 km ( R HF 0 13.94km). The influence of the approximations, parameter sets and hyperons on the neutron star's moment of inertia is exhibited.

Phonon excitations in multicomponent amorphous solids

The method of two-time temperature-dependent Green's functions is used to investigate phonon excitations in multicomponent amorphous solids. The equation obtained for the energy spectrum of the phonon excitations takes into account the damping associated with scattering of phonons by structure fluctuations. The quasicrystal approximation is considered, and as an example explicit expressions are obtained for the case of a two-component amorphous solid for the frequencies of the acoustical and optical modes and for the longitudinal and transverse velocities of sound. The damping is investigated.

Theory of knight shift due to indirect nuclear hyperfine interactions

We derive a theory of Knight shift ( K) in solids including the effects of periodic potential, spin-orbit interaction, magnetic hyperfine interactions and indirect nuclear hyperfine interaction. We use a temperature dependent Green's function technique to evaluate the thermodynamic potential which is then used to obtain a general expresion for the Knight shift. Our formula for K is expressed as a sum of contributions due to conduction electrons and localized electrons of either d- or f-type: K cond and K loc. While K cond is the same as our previous expression for K derived in the absence of localized magnetic moments, K loc is a new contribution and is due to the hybridization of conduction and localized electron magnetic moments. We also briefly discuss the many-body effects on the different contributions to K. Finally, the importance of the present theory in possible applications to metals, alloys and compounds containing transition and rare-earth elements, and magnetic semiconductors is discussed.

Theory of magnetic susceptibility of Bloch electrons in the presence of localized magnetic moments.

We derive a theory of magnetic susceptibility (\ensuremath{\chi}) of Bloch electrons including the effects of periodic potential, spin-orbit interaction, and localized magnetic moments. We use a temperature-dependent Green's-function technique to evaluate the thermodynamic potential which is then used to obtain a general expression for \ensuremath{\chi}. Our formula for \ensuremath{\chi} is expressed as \ensuremath{\chi}=${\ensuremath{\chi}}_{\mathrm{MK}+\mathrm{P}{\ensuremath{\chi}}_{\mathrm{CW}}}$, where ${\ensuremath{\chi}}_{\mathrm{MK}}$ is the magnetic susceptibility of Bloch electrons obtained by Misra and Kleinman, which includes spin, orbital, and spin-orbit contributions, P is the shift in the electron paramagnetic resonance frequency, and ${\ensuremath{\chi}}_{\mathrm{CW}}$ is the Curie-Weiss susceptibility. The second term, which is obtained for the first time by us, is due to the interaction of conduction-electron magnetic moment and the localized magnetic moments. Many-body effects, although not included from first principles, are discussed on the final results of \ensuremath{\chi}, in view of their importance. We also discuss the importance of the theory in possible applications. Finally, we believe that the theory presented in this work is the most general and thorough treatment which has yet been made of this problem.